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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 79 (page 411)

Find the average rate of change offfrom $0$ torole="math" localid="1646561530009" $\frac{蟺}{2}$ .
role="math" localid="1646561569314" $f (x) = \sin (\frac{x}{2})$

Short Answer

Expert verified

The average rate of change of $f (x) = \sin (\frac{x}{2})$ from $0$ to $\frac{蟺}{2}$ is $\frac{\sqrt{2}}{蟺}$

Step by step solution

01

Step 1. Given data

The given function is

$f (x) = \sin (\frac{x}{2})$

The given interval is $(0, \frac{蟺}{2})$

02

Step 2. The average rate of change

Consider $(a, b) = (0, \frac{蟺}{2})$

The average rate of change of f

role="math" localid="1646562090430" $\frac{f (b) - f (a)}{b - a} = \frac{f (\frac{蟺}{2}) - f (0)}{\frac{蟺}{2} - 0} = \frac{\sin (\frac{\frac{蟺}{2}}{2}) - \sin (\frac{0}{2})}{\frac{蟺}{2} - 0} = \frac{\sin (\frac{蟺}{4}) - \sin (0)}{\frac{蟺}{2}} = \frac{\frac{1}{\sqrt{2}} - 0}{\frac{蟺}{2}} = \frac{\sqrt{2}}{蟺}$

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Most popular questions from this chapter

For a circle of radius r, a central angle of u degrees subtends an arc whose length s is $s = \frac{蟺}{180} r 胃$ . Discuss whether this is a true or false statement. Give reasons to defend your position.

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

Convert each angle in degrees to radians. Express your answer as a multiple of $蟺$ .

$30 掳$

The Montauk Point Lighthouse on Long Island has dual beams (two light sources opposite each other). Ships at sea observe a blinking light every five seconds. What rotation speed is required to do this?

Convert angle in radian to degree-

$4 蟺$

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